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13 Nov 2019
1. A yam is put in a hot oven, maintained at a constant temperature 218°C. At time t 40 minutes, the temperature T of the yam is 166 C, and is increasing at a (instantaneous) rate of 2°/min. Newton's law of cooling (or, in our case, warming) implies that the temperature at time t is given by T(t) = 218-aa" Find a, and b. Round your answer for a to one decimal place. Round your answer for b to three decimal places. 2. The sum of three nonnegative numbers is 36, and one of the numbers is twice one of the other numbers. What is the maximum value of the product of these three numbers? 3. Four feet of wire is to be used to form a square and a circle. How much of the wire should be used for the square and how much should be used for the circle to enclose the maximum total area. . The summer of 2000 was devastating for forests in the western US: over 3.5 million acres of trees were lost to fires, making this the worst fire season in 30 years. This question examines a fire management technique called firebreaks, which reduce the damage done by forest fires. A firebreak is a strip where trees have been removed in a forest so that a fire started on one side of the strip will not spread to the other side. Having many firebreaks helps confine a fire to a small area. On the other hand, having too many firebreaks involves removing large swaths of trees. A forest in the shape of a 50 km by 50 km square has firebreaks in rectangular strips 50 km by 0.01 km. The trees between two firebreaks are called a stand of trees. All firebreaks in this forest are parallel to each other and to one edge of the forest, with the first firebreak at the edge of the forest. The firebreaks are evenly spaced throughout the forest. (For example, the figure below shows four firebreaks.) The total area lost in the case of a fire is the area of the stand of trees in which the fire started, plus the area of all the firebreaks
1. A yam is put in a hot oven, maintained at a constant temperature 218°C. At time t 40 minutes, the temperature T of the yam is 166 C, and is increasing at a (instantaneous) rate of 2°/min. Newton's law of cooling (or, in our case, warming) implies that the temperature at time t is given by T(t) = 218-aa" Find a, and b. Round your answer for a to one decimal place. Round your answer for b to three decimal places. 2. The sum of three nonnegative numbers is 36, and one of the numbers is twice one of the other numbers. What is the maximum value of the product of these three numbers? 3. Four feet of wire is to be used to form a square and a circle. How much of the wire should be used for the square and how much should be used for the circle to enclose the maximum total area. . The summer of 2000 was devastating for forests in the western US: over 3.5 million acres of trees were lost to fires, making this the worst fire season in 30 years. This question examines a fire management technique called firebreaks, which reduce the damage done by forest fires. A firebreak is a strip where trees have been removed in a forest so that a fire started on one side of the strip will not spread to the other side. Having many firebreaks helps confine a fire to a small area. On the other hand, having too many firebreaks involves removing large swaths of trees. A forest in the shape of a 50 km by 50 km square has firebreaks in rectangular strips 50 km by 0.01 km. The trees between two firebreaks are called a stand of trees. All firebreaks in this forest are parallel to each other and to one edge of the forest, with the first firebreak at the edge of the forest. The firebreaks are evenly spaced throughout the forest. (For example, the figure below shows four firebreaks.) The total area lost in the case of a fire is the area of the stand of trees in which the fire started, plus the area of all the firebreaks
Elin HesselLv2
20 Aug 2019